二阶非线性泛函微分方程解的振动性质

研究了一类二阶非线性泛函微分方程解的振动性以及非振动解的有界性.在一定条件下,建立了几个新的振动性和有界性定理,其结果推广和改进了已有的一些结果.     

三阶非线性泛函微分方程振动的比较准则

本文利用比较法,与一阶时滞微分方程的振动性相比较,研究一类三阶非线性泛函微分方程的振动性,建立该类方程振动的新比较振动准则.本文结果推广和改进了最近文献中的一些新结果.     

脉冲时滞抛物型方程解的振动性

本文研究了两类边界条件下有振动系数的脉冲时滞抛物型方程解的振动性,得到了若干解振动的判别准则。其结果即使用于有固定符号系数的方程,也显著地改进了已有的结果。     

具有振动系数时滞差分方程解的振动性

本文研究了一类具振动系数时滞差分方程解的振动性,给出了一个新的振动准则,改进了已有文献中许多相关的结果．     

一类二阶线性微分方程的振动性及非振动性

本文研究了二阶线性方程的振动性及非振动性问题，建立了若干新的振动与非振动性结果，它们改进并推广了若干已知的定理。     

带强迫项的脉冲时滞微分方程的振动性

研究带一阶强迫项的脉冲时滞微分方程的振动性,借助于Kartsatos变换,得到了若干判别这类方程振动的充分性条件,所得的结果推广并改进了时滞微分方程振动性理论中某些已知的相关结果。     

一类高阶非线性泛函微分方程的振动性

给出了一类高阶非线性泛函微分方程的若干振动定理,推广了文献中的一些振动结果.     

高阶具非线性中立项不稳定型时滞微分方程的振动性和非振动性

在α>1,且0<β<α情性下研究了高阶具非线性中立项不稳定型时滞微分方程[x(t)-pxα(t-τ)](n)=q(t)xβ(t-σ),(t≥t0)的振动和非振动性.利用一些新的技巧,获得了上述方程有界解振动的振动准则和至少存在一个非振动解的非振动准则,所得结果补充和推广了已有文献部分结果.     

具有“弱积分小”系数的二阶椭圆型偏微分方程解的振动性质

本文考虑二阶非线性椭圆型偏微分方程解的振动性质，得到了在具有“弱积分小”系数条件下，所有解均振动的充分准则，这些结果在很大程度上改进和推广了具有“积分小”系数的二阶常微分方程的振动结果．     

脉冲中立型时滞微分方程的振动性

本文证明了线性脉冲中立型微分方程解的振动性等价于一类线性非脉冲中立型时滞微分方程解的振动性.应用这一结果,建立了线性脉冲中立型方程解振动性的显式判据.这些判别条件,显著地改进了已有的结果.     

Oscillation criteria of a class of fourth order differential equations

In the present paper, we consider the oscillation of a class of self‐adjoint fourth order differential equation. Some oscillation and non‐oscillation criteria on a perturbation equation of Euler differential equation are given. In particular, we find the exact value of a constant in some oscillation criteria, which has answered the open problem presented by Do?lý in 2004. Copyright © 2011 John Wiley & Sons, Ltd.     

Relative oscillation of linear Hamiltonian differential systems

We discuss the concept of relative oscillation for linear Hamiltonian differential systems. We prove a statement which enables to study this oscillation using the criteria of the classical oscillation theory. We also discuss some other aspects of the problem.     

Oscillations of nonlinear hyperbolic equations with functional arguments via Riccati method

This paper is devoted to the study of the oscillatory behavior of solutions of nonlinear hyperbolic equations with functional arguments by using integral averaging method and a generalized Riccati technique. First, we establish oscillation results for nonlinear hyperbolic equations by applying oscillation criteria for Riccati inequality. Secondly, we present interval oscillation results for nonlinear hyperbolic equations. These results improve and extend oscillation results of Cui and Xu [1].     

一类二阶非线性变时滞微分方程的振动准则

研究二阶非线性变时滞微分方程x″(t)+p(t)f(x(g(t)))=0,对振动因子p(t)变符号的情况讨论了方程的振动性,通过两个已有引理得到了方程振动的两个充分条件.所得结论推广了原有的二阶非线性微分方程与变时滞微分方程当系数不变号时的振动性结论,完善了具变符号振动因子的二阶非线性变时滞微分方程的研究.     

一类脉冲中立型抛物系统振动性

考虑一类具高阶Laplace算子的脉冲中立型抛物偏微分系统的振动性,借助于一阶脉冲时滞微分不等式,得到了该类系统在Dirichlet边值条件下所有解振动的若干充分条件.所得结果充分反映了脉冲和时滞在系统振动中的影响作用.     

Oscillation behavior of solution of impulsive fractional differential equation

In this paper, we study the oscillation of impulsive Caputo fractional differential equation. Sufficient conditions for the asymptotic and oscillation of the equation are obtained by using the inequality principle and Bihari Lemma. An example is given to illustrate the results. This is the first time to study the oscillation of impulsive fractional differential equation with Caputo derivative.     

脉冲时滞抛物型偏微分方程组解的振动性

研究一类脉冲时滞抛物型偏微分方程组解的振动性,利用一阶脉冲时滞微分不等式获得了该类方程组在两类不同边值条件下所有解振动的若干充分条件.所得结果充分反映了脉冲和时滞在振动中的影响作用.     

脉冲中立型时滞抛物偏微分方程组的振动准则

考虑一类脉冲中立型时滞抛物偏微分方程组解的振动性,利用一阶脉冲时滞微分不等式获得了该类方程组在Robin,Dirichlet边值条件下所有解振动的若干充分条件.所得结果充分反映了脉冲和时滞在振动中的影响作用.     

具多偏差变元的一阶泛函微分方程的振动性

本文首先考虑多时滞泛函微分方程的振动性,给出了方程振动的几个新的充分条件.然后,把这些结果推广到微分不等式,并应用于多时滞中立型方程的振动性.     

On oscillation of nonlinear second-order differential equations with damping term

The paper is concerned with oscillation of a novel class of nonlinear differential equations with a damping term. First it is demonstrated how known oscillation results for another intensively studied class of equations can be translated to the one in question, and vice versa. Advantages and drawbacks of such translation are carefully examined. Then an oscillation criterion for the new class of equations is established. The principal result of the paper is compared to those reported in the literature, and an illustrative example to which known oscillation criteria fail to apply is provided.